Effectiveness of Problem-Solving as a Teaching Strategy in Enhancing Students’ Conceptual Understanding and Critical Thinking in Mathematics Education

Source abstract

In order to improve students’ conceptual understanding and critical thinking skills in mathematics education, this study looks at the problem-solving approach as an instructional tool. Mathematics is a content-focused subject that requires students to think, evaluate, and even apply concepts in the real world. It cannot be reduced to simply memorizing formulas and following algorithms. However, the predominant teaching approach in Pakistan, like in many other school systems, is rote memorization, which leaves little room for inquiry or higher order thinking. The aim of this study was to investigate whether employing problem-solving techniques could serve as a “bridge” between these levels, allowing senior secondary school pupils to learn more deeply. Three hundred Grade 9 students from public and private schools in three districts in southern Punjab participated in a quasi-experimental study using a pretest-posttest control group design. After being split up into two groups, the subjects studied the same material, with the first group using a problem-solving approach and the second group listening to a traditional lecture. Two standardized tools were used to collect the data: the Mathematical Critical Thinking Assessment (MCTA), which consists of 20 context problems to measure skills in appropriate reflection of thinking, evaluation, and decision making, and the Conceptual Understanding Test (CUT), which consists of 25 test items to assess algebraic reasoning and understanding. Cronbach’s α values for both instruments were 0.87 and 0.89, respectively, indicating good reliability. The study was conducted for 8 weeks, the experiment group received RMT, collaborative discussion, reflexive task while the control group followed conventional textbook teaching method. Statistical analysis The data were analyzed using the SPSS Version 26 software which employed descriptive statistics, independent and paired sample t-test, (ANOVA) and Pearson correlation test. The experimental and control groups had significantly different (t = 9.52, p <. 001) and a mean of 18.6 point improvement. Additionally, we found a robust positive association (r = 0.71, p <. 001) between CT and conceptual understanding was found, indicating that they are interrelated. These results show that problem-solving has a positive impact on conceptual understanding, logical reasoning and critical reflection abilities of students. The method not only increases academic achievement but also teaches students how to think critically and creatively. This study is in favor of constructivist theory, which claims that learners do not receive passively knowledge, but rather they achieve it interactively and reflectively. Apart from this, it also has the following practical implications for mathematics educators, administrators and curriculum developers : problem-solving pedagogies should be built in to curricula of mathematics educations as well as teacher education. The author argues that problem-solving approach is ideal teaching and learning strategy because it triggers curiosity, makes learning experiences meaningful, and also help students acquire metaphysical reasoning and mental tools needed in the twenty-first century.